After a certain point the difference between the canard deflection angle and angle of attack are too great for the downwash effect to occur. If the canard sustains the difference in angle between itself and the wing it will stall out first, which then disrupts the downwash which then stalls the wing. That or the canard has to deflect downward to prevent over pitching. Both induce a lot of extra drag that isn't overcompensated by extra lift, which hurts the lift drag ratio. LERXes don't have this problem because they generate vortices a different way, but their problem is that they don't begin generating vortices until they've reached a certain angle of attack, and (if I'm not wrong about this point) the inability to terminate that down wash means that an aircraft will have to employ other draggier methods to prevent over pitching. My understanding is the PAK-FA tried to get the best of both worlds by adopting LEVCONS. I suspect the J-20s design may be a different approach to achieve that same purpose.
It is hard to understand how canard works because everything about the canard is so counter-intuitive. Canard deflects downward when the aircraft is at large angle-of-attack, which reduces pitching moment. In that situation, the angle-of-attack that canard makes with respect to the airstream is actually small.
You can imagine that the canard always sits around low angle-of-attack regardless of how the aircraft orientates. As a result, the amount of lift contributes by the canard is relatively constant. This differs from vortex lift of a leading extension which is affected more by angle-of-attack. For that same reason, canard also produces lower drag. I have highlighted the relevant curves in red in the following graphs.
Tailplane cannot compete with canard at high angle-of-attack, because tailplane would need to go into even bigger angle-of-attack to force the aircraft's nose down. The problem in that situation is that the tailplane goes into stall, and pitch control is lost.
As to LEVCON on that PAKFA, that's actually the poor man's solution to canard. Canard affects more variables, so is more difficult to design, more expensive, and can result in deadly consequences if not designed properly.
